Some actors are lucky. In the third act of their careers, they become dream versions of their own parents, or grandparents. Paul Newman did that. So did Katharine Hepburn. We got to know them, and love them, at one age; then, against every Hollywood dictum, they were allowed to mature, to mellow, as they acquired a few more years. They weren't competing with their iconic youthful images so much as putting our memories of those early years to good use, as the crow's feet, slowed gait and thinning hair came along and changed them. It's a privilege to watch an actor age gracefully in the movies; so few are given the chance or the roles.

Robert Redford is a slightly different case.

He's not aging gracefully; he's aging supernaturally. He's now 76. He looks terrific, and it's movie-star terrific, which makes it harder for him to figure out how to play an ordinary (or even extraordinary) character who happens to be getting on. The copious and permanently wind-swept hair remains ready for its close-up, and there's a moment in Redford's new film "The Company You Keep" when his character, a '60s radical long in hiding and wanted for murder, runs down a dark street at night, thinking he's being followed. It's as if the Redford of "All the President's Men" nearly 40 years ago never stopped running once he met with Hal Holbrook in that D.C. parking garage.

Taken from a novel by Neil Gordon, "The Company You Keep" is livelier than the last couple of films directed by Redford, "Lions for Lambs" and "The Conspirator." It's best enjoyed as an actors' showcase. Premise: Redford is Jim Grant, a progressive public interest lawyer living in Albany, N.Y. He's a widower (the wife in the novel wasn't dead, just a trashy mess of an ex) raising a preteen daughter on his own. Then a cub reporter (Shia LaBeouf) ferrets out the truth on this man: He's really a former member of the bomb-throwing, bank-robbing Weather Underground anti-war collective.

So Jim runs. He has his name to clear and a daughter to protect. Jim and the reporter, Ben, become ideological frenemies of a sort, taunting each other with arguments of liberal idealism versus apolitical cynicism. The Redford character darts across the country, contacting his former Weather Underground associates, with the purpose of finding his great love, the one they call Mimi, who now smuggles marijuana for a comfortable living and who considers her old flame a sellout to the cause.

Mimi's played by Julie Christie, whose beauty remains undimmed by the years. Better still, it's a face that hasn't been messed with. She looks her age, even if her character as written by screenwriter Lem Dobbs is a smug finger-wagger.

The movie as a whole is like that. (If its brand of liberal despair feels strident to a liberal, I don't know what the other half of the country will make of "The Company You Keep.") Wisely, though, the story acknowledges a full and fractious spectrum of lefty-ism, from Grant's nonviolence credo to the "burn, baby, burn" mentality of some of his colleagues. Nick Nolte shows up for a couple of scenes as one ex-Weather member, and though I couldn't catch most of his dialogue, it's always a pleasure to watch him. Richard Jenkins enjoys himself as a jumped-up Bill Ayers-type revolutionary now teaching on the university level. Terrence Howard plays the FBI agent on the hunt.

The novel was a digital epistolary, told through emails written by the protagonist to his teenage daughter. The movie struggles to turn the story into a paradoxical easygoing thriller, befitting the age bracket of its key ensemble members. The other half of "The Company You Keep," the one with LaBeouf digging for clues to his quarry's past, features such worthy young talents as Brit Marling and Anna Kendrick. But this is Redford's show, and Christie's, and Jenkins'. And Susan Sarandon's. And when Brendan Gleeson shows up, his scenes may be exposition-heavy and not particularly well-written, but you think: Good old Brendan Gleeson. There's a face.